Geographically Weighted Regression Using a Non-Euclidean Distance Metric

1. Geographically Weighted Regression Using a Non-Euclidean Distance Metric Research presented in this paper was jointly funded by a Strategic Research Cluster grant (07/SRC/I1168) by Science Foundation Ireland under the National Development Plan. The authors gratefully acknowledge their support. Road network data of London provided by Ordnance survey GWR is proposed as a kind of local technique to estimate regression models with spatially varying relationships. It makes a point-wise calibration with especially concerning a ‘bump of influence’: around each regression point nearer observations have more influence in estimating the local set of parameters than observations farther away. a basic GWR model for each regression point icould be written as: The calibration is made in a point-wise mode, and for each location i the regression coefficients are estimated via the following matrix calculation. Geographically Weighted Regression Acknowledgements Calibrated105 GWR models with dependent variable “PURCHASE” and independent variables from the combinations of the rest 14 factors National Centre for Geocomputation, NUI Maynooth, Co.Kildare, Ireland A sample of 2108 properties sold within London during 2001 Case study using Network distance Introduction Geographically Weighted Regression (GWR) is a local modelling technique to makes a point-wise calibration around each regression point using a ‘bump of influence’: around each regression point nearer observations have more influence in estimating the local set of parameters than observations farther away. Until now, the Euclidean distance (ED) (straight line distance) has generally been adopted as the default for GWR applications. However, The degree of connectedness between two places may not be optimally represented by a straight line. For example, an area might be divided by a river or buildings and connected internally by bridges or roads; surface distance would be more reasonable in a mountainous area. In this work, we are focusing on how to use non-Euclidean distance metrics for calibrating a GWR model , and evaluate their performance in case studies. Binbin Lu Data sources Calibrations of GWR models Standard GWR calibration Euclidean distance (Straight line distance) Comparison of Akaike Information Criterion (AIC) between calibrations with Euclidean distance (ED) and results from using network distance (ND) Non-Euclidean geographical distance metrics ... Great circle distance Network distance Manhattan distance Cost distance Estimation of parameter FLOORSZ fitted with Euclidean distance Estimation of parameter FLOORSZ fitted with Network distance